Effect of global FCFS and relative load distribution in two-class queues with dedicated servers

Abstract

In this paper, we investigate multi-class multi-server queueing systems with global FCFS policy, i.e., where customers requiring different types of service -provided by distinct servers -are accommodated in one common FCFS queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered by customers of other classes. The purpose of this paper is twofold: to gain (qualitative and quantitative) insight into the impact of (i) the global FCFS policy and (ii) the relative distribution of the load amongst the customer classes, on the system performance. We therefore develop and analyze an appropriate discrete-time queueing model with general independent arrivals, two (independent) customer classes and two class-specific servers. We study the stability of the system and derive the system-content distribution at random slot boundaries; we also obtain mean values of the system content and the customer delay, both globally and for each class individually. We then extensively compare these results with those obtained for an analogous system without global FCFS policy (i.e., with individual queues for the two servers). We demonstrate that global FCFS, as well as the relative distribution of the load over the two customer classes, may have a major impact on the system performance.

Performance analysis of a continuous-time two-class global first-come-first-served queue with two servers and presorting

“…In Mélange et al (2011), Bruneel et al (2013), Bruneel et al (2012), the blocking effect caused by the gFCFS service discipline is thoroughly researched in both continuous and discrete time. Here we already quantified the often devastating effect in system performance.…”

Analysis of a two-class continuous-time queueing model with two tandem dedicated servers

“…We refer to Bruneel et al [1] for more details of those applications. Then, Bruneel et al [2] continued to investigate the effect of gFCFS and relative load distribution in two-class queues with dedicated servers. In [2], they gave the stability condition of the system and derived the system size distribution at random slot boundaries.…”

“…Then, Bruneel et al [2] continued to investigate the effect of gFCFS and relative load distribution in two-class queues with dedicated servers. In [2], they gave the stability condition of the system and derived the system size distribution at random slot boundaries. Recently, Mélange et al [3] went on considering a continuous-time queueing model with class clustering (customers of the same type having the tendency to arrive "back-to-back") and gFCFS policy, where customers of different types have the same service rate μ, and gave the system size distribution and sojourn time distribution of an arbitrary customer.…”